Statistics
Mean Median Mode Calculator: Find The Average, Median, Mode And Range
Last updated: October 2026
Written by Jessica Hill
A mean median mode calculator finds three measures of center for a list of numbers. The mean is the average: add the numbers and divide by how many there are. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. The range is the largest minus the smallest.
- Free, no sign-up
- Shows the working
- Runs on your device
Mean, median and mode answer the same question in three ways: what is a typical value in this data? They often give different answers, and knowing which one to trust is the real skill. This guide covers how to find each one, plus range, weighted averages, other kinds of averages and grouped data. Every example was checked in Python.
Note: Calc Solver (calc-solver.co) is an independent guide site and is not affiliated with any calculator mentioned here.
What Mean, Median And Mode Mean
Mean, median and mode are called measures of central tendency. Each one describes the center of a data set in a different way.
| Measure | What it is | Best for |
|---|---|---|
| Mean | The sum divided by the count | Data without extreme values, like test scores in a class |
| Median | The middle value when sorted | Data with outliers, like home prices or incomes |
| Mode | The most common value | Categories or repeated values, like shoe sizes or survey answers |
| Range | Largest minus smallest | Showing how spread out the data is |
In everyday speech, "average" usually means the mean. So an average calculator and a mean calculator do the same thing. In statistics, though, "average" can refer to any of the three.
How To Use The Mean Median Mode Calculator
The calculator above works for simple lists, weighted grades and grouped data.
- Pick a tab. Data Set for a plain list of numbers, Weighted Average when some values count more, or Grouped Data for a frequency table.
- Enter your numbers. Type them with commas or spaces, or paste a column straight from Excel or Google Sheets.
- Read the results. You get every measure at once, with the steps for each.
We will use one data set through most of this guide: 13, 16, 12, 14, 19, 12, 14, 13, 14.
How To Find The Mean (Average)
To find the mean, add all the values and divide by how many values there are. The formula is mean = Σx ÷ n, where Σx is the sum and n is the count.
For 13, 16, 12, 14, 19, 12, 14, 13, 14:
- Add: 13 + 16 + 12 + 14 + 19 + 12 + 14 + 13 + 14 = 127.
- Count: there are 9 values.
- Divide: 127 ÷ 9 = 14.11 (rounded).
The mean does not have to be one of the numbers in the list, and it often is not a whole number. A mean of 14.11 is perfectly normal.
Sample mean vs population mean. The calculation is the same, but the symbols differ. If your data covers every member of a group, like every student in one class, it is a population, and the mean is written μ (mu). If it is only part of a larger group, like 50 students surveyed out of a whole school, it is a sample, and the mean is written x̄ (x-bar). The difference matters later, for standard deviation, where samples divide by n − 1 instead of n.
How To Find The Median
To find the median, sort the numbers from smallest to largest and take the middle one. If there is an even number of values, the median is the average of the two middle values.
Odd count: sorted, our data is 12, 12, 13, 13, 14, 14, 14, 16, 19. With 9 values, the 5th value is the middle. The median is 14.
Even count: for 3, 7, 8, 12, the two middle values are 7 and 8. The median is (7 + 8) ÷ 2 = 7.5.
A quick way to find the middle position is (n + 1) ÷ 2. For 9 values, that is position 5. For 4 values, it is position 2.5, which means "halfway between the 2nd and 3rd values."
The most common mistake is forgetting to sort first. The middle of the unsorted list 13, 16, 12, 14, 19 is 12, but the true median is 14.
How To Find The Mode
To find the mode, count how often each value appears. The value with the highest count is the mode.
For our data, a frequency table makes it clear:
| Value | 12 | 13 | 14 | 16 | 19 |
|---|---|---|---|---|---|
| Count | 2 | 2 | 3 | 1 | 1 |
The value 14 appears 3 times, more than any other, so the mode is 14.
A data set can have more than one mode, or none at all:
| Type | Example | Mode |
|---|---|---|
| Unimodal (one mode) | 13, 16, 12, 14, 19, 12, 14, 13, 14 | 14 |
| Bimodal (two modes) | 2, 4, 4, 6, 6, 9 | 4 and 6 |
| Multimodal (three or more) | 1, 1, 2, 2, 3, 3, 5 | 1, 2 and 3 |
| No mode | 1, 2, 3 | None, since every value appears once |
The mode is the only measure of center that works for non-number data. If a survey asks for a favorite color, you cannot average colors, but you can find the most popular one.
How To Find The Range And Midrange
The range shows how spread out the data is: range = maximum − minimum. The midrange is the point halfway between them: midrange = (maximum + minimum) ÷ 2.
For our data, the maximum is 19 and the minimum is 12:
- Range: 19 − 12 = 7
- Midrange: (19 + 12) ÷ 2 = 15.5
The range is easy to find but sensitive to one unusual value. If a single 50 is added to the list, the range jumps from 7 to 38, even though the other values did not change.
Mean Vs Median Vs Mode: Which Should You Use?
Use the mean for balanced data, the median when there are outliers or the data is lopsided, and the mode for categories or the most common choice.
Outliers show the difference clearly. Five salaries at a small company are $40,000, $45,000, $50,000, $55,000 and $1,000,000 (the owner):
- Mean: $238,000
- Median: $50,000
The mean is pulled far up by one value and describes nobody's real pay. The median shows what a typical worker earns. That is why home prices and household incomes are usually reported as medians.
The gap between mean and median also tells you the shape of the data:
| Pattern | Shape | Example |
|---|---|---|
| Mean ≈ median | Roughly symmetric | Heights of adults |
| Mean > median | Skewed right (long tail of high values) | Incomes, home prices |
| Mean < median | Skewed left (long tail of low values) | Scores on an easy test |
How To Calculate A Weighted Average
A weighted average gives some values more importance than others. Multiply each value by its weight, add the results, then divide by the total of the weights.
weighted average = Σ(value × weight) ÷ Σ(weight)
Course grades are the classic example. Homework is 20 percent of the grade, tests are 50 percent and the final exam is 30 percent. A student scores 90, 78 and 85:
| Category | Score | Weight | Score × weight |
|---|---|---|---|
| Homework | 90 | 0.20 | 18.0 |
| Tests | 78 | 0.50 | 39.0 |
| Final | 85 | 0.30 | 25.5 |
| Total | 1.00 | 82.5 |
The weighted average is 82.5. A plain average of 90, 78 and 85 would be 84.33, which overstates the grade because the low test score counts for half the course.
GPA works the same way, with credit hours as weights. A 4-credit A counts twice as much as a 2-credit A. If your weights are percentages, the percentage calculator can help you convert them to decimals.
Other Kinds Of Averages
The ordinary mean is called the arithmetic mean. Two other averages give better answers in certain situations.
Geometric mean for growth rates. Use it to average percentages that multiply over time, like investment returns or population growth. If something gains 10 percent one year and loses 10 percent the next, the arithmetic mean says 0 percent. But 1.10 × 0.90 = 0.99, so you actually lost 1 percent. The geometric mean, √(1.10 × 0.90) ≈ 0.995, shows the true average change: about −0.5 percent per year.
Harmonic mean for rates and speeds. Use it to average rates over the same distance. If you drive to a town at 60 mph and back at 40 mph, your average speed is not 50 mph. The harmonic mean, 2 ÷ (1/60 + 1/40), gives 48 mph, because you spend more time at the slower speed.
For square roots and powers in these formulas, the scientific calculator handles each step.
Mean, Median And Mode For Grouped Data
When data comes in a frequency table with ranges (classes) instead of exact values, you can only estimate the mean, median and mode. Each estimate uses the midpoints or boundaries of the classes.
Here are the test scores of 30 students, grouped by tens:
| Class | Frequency (f) | Midpoint (x) | f × x | Cumulative frequency |
|---|---|---|---|---|
| 0–10 | 5 | 5 | 25 | 5 |
| 10–20 | 8 | 15 | 120 | 13 |
| 20–30 | 12 | 25 | 300 | 25 |
| 30–40 | 5 | 35 | 175 | 30 |
| Total | 30 | 620 |
Estimated mean: Σ(f × x) ÷ Σf = 620 ÷ 30 ≈ 20.67.
Estimated median: the middle position is n ÷ 2 = 15. The cumulative frequency passes 15 in the 20–30 class. Use median = L + ((n ÷ 2 − F) ÷ f) × w, where L is the class's lower boundary (20), F is the cumulative frequency before it (13), f is its frequency (12), and w is the class width (10). That gives 20 + (2 ÷ 12) × 10 ≈ 21.67.
Estimated mode: the modal class is 20–30, since it has the highest frequency. A common estimate is L + ((f₁ − f₀) ÷ ((f₁ − f₀) + (f₁ − f₂))) × w, where f₁ is the modal class frequency (12), f₀ the class before (8) and f₂ the class after (5). That gives 20 + (4 ÷ 11) × 10 ≈ 23.64.
How To Find Mean, Median And Mode In Excel Or On A Calculator
Spreadsheets and graphing calculators have built-in functions for these measures.
| Tool | Mean | Median | Mode |
|---|---|---|---|
| Excel and Google Sheets | =AVERAGE(A1:A9) | =MEDIAN(A1:A9) | =MODE.SNGL(A1:A9), or =MODE.MULT for several modes |
| TI-84 | STAT, enter data in L1, then STAT > CALC > 1-Var Stats | Shown as Med in 1-Var Stats | Not built in. Sort the list and count |
Excel's MODE.SNGL returns only the first mode it finds. If your data is bimodal, use MODE.MULT so you do not miss the second one.
How To Find A Missing Value From The Mean
If you know the mean and all but one value, you can work backward to find the missing value. Multiply the mean by the count to get the total, then subtract the values you know.
You need an average of 85 across three tests and you scored 80 and 90 on the first two. The total must be 85 × 3 = 255. You have 80 + 90 = 170 so far. So you need 255 − 170 = 85 on the third test.
This trick answers questions like "what do I need on the final?" and "how many points to raise my average?" It works for any average, as long as each value counts equally.
Common Mean, Median And Mode Mistakes
Most errors come from skipping a step or using the wrong measure.
| Mistake | Example | Fix |
|---|---|---|
| Not sorting before finding the median | Median of 13, 16, 12 = 16 | Sort first: 12, 13, 16, so the median is 13 |
| Forgetting to average the two middle values | Median of 3, 7, 8, 12 = 7 | Use (7 + 8) ÷ 2 = 7.5 |
| Dividing by the wrong count | Missing a 0 or a repeated value | Count every value, including zeros and repeats |
| Listing only one mode | Mode of 2, 4, 4, 6, 6, 9 = 4 | Both 4 and 6 are modes |
| Calling 1, 2, 3 "mode = 1" | Every value appears once | There is no mode |
| Using a plain mean for weighted grades | (90 + 78 + 85) ÷ 3 | Use the weights: 82.5 |
| Using the mean with big outliers | Mean salary $238,000 | Report the median: $50,000 |
Summary
- The mean is the sum divided by the count. The median is the middle sorted value. The mode is the most common value. The range is max minus min.
- Use the median when outliers pull the mean, and the mode for categories.
- A weighted average multiplies each value by its weight before dividing by the total weight.
- Geometric means fit growth rates, and harmonic means fit average speeds.
- Grouped data uses midpoints and class boundaries to estimate all three measures.
Next step: paste your numbers into the mean median mode calculator at the top of this page. For mixed numbers in your data, the fraction calculator helps, or explore every tool on the Calc Solver homepage.
Frequently Asked Questions
Is the average the same as the mean?
Usually, yes. In daily life and on most calculators, "average" means the arithmetic mean: the sum divided by the count. In statistics, "average" is a broader word that can include the median and mode too. If a report says "average home price," check whether it means the mean or the median, since the two can be very different.
Can the mean, median and mode all be the same?
Yes. In a perfectly symmetric data set with one peak, like 2, 3, 3, 3, 4, all three equal 3. Real data that follows a bell curve, such as many test scores or heights, often has a mean, median and mode that are close together. When they differ a lot, the data is probably skewed.
What if every number in the set is the same?
If every value is identical, like 7, 7, 7, 7, then the mean, median and mode are all 7, and the range is 0. Some textbooks say a set where every value appears equally has no mode. Here, though, every value is the same single number, so 7 is the mode. The midrange is also 7.
How do outliers affect the mean, median and mode?
Outliers have the biggest effect on the mean and the range, because every value is part of the sum. The median barely moves, since it only depends on the middle position. The mode does not change at all unless the outlier is repeated. That is why the median is preferred for data like incomes and home prices.
Do I include zeros when finding the mean?
Yes, if the zero is a real value. A test score of 0 or a day with $0 in sales is data, and it should be added to the sum and counted. Leaving it out would make the mean too high. Only skip a blank if it means "no data," such as a test that was not taken.
Try it with your own numbers
The calculator at the top of this page uses the same formulas as the examples.